基于泰勒展开式的模糊微分方程数值解法

Numerical method for solving fuzzy differential equations based on Taylor expansion

由刘过程驱动的模糊微分方程是处理模糊动态问题的重要工具,在求解由刘过程驱动的模糊微分方程时,有一些模糊微分方程并不能求出其解析解,这时往往需要研究一些可以求出模糊微分方程近似解的方法.本文利用模糊Taylor展开式,给出了一种基于模糊Taylor展开式的模糊微分方程数值解法,并证明了该数值解法的收敛性.

Fuzzy differential equation driven by Liu process is an important tool to deal with dynamic fuzzy problem.When solving fuzzy differential equation,the analytical solution for some fuzzy differential equation driven by Liu process can’t be obtained sometimes,thus it is necessary for us to discuss the numerical method in most situations.In this paper,a numerical method for solving fuzzy differential equation based on fuzzy Taylor expansion is given and its convergence is also proved.